Both Narine and Pollard are contracted in the Australian Big Bash, which takes place from December 9 to January 19, while the Caribbean T20 is set for January 6-20.
Pollard was recruited by Adelaide Strikers for the 2011/2012 Big Bash, but the allrounder was ruled out of the tournament due to injury.
Narine, who was the Player of the Tournament in the Indian Premier League (IPL) this year, was contracted by Sydney Sixers for the 2012/2013 Big Bash.
Bravo is recovering from an injury he picked up during the West Indies ICC T20 World Cup in Sri Lanka.
Asked if T&T will have the services of the trio, Ramkessoon said: “I don’t know at this point in time. We will have to communicate with them and find out their availability based on their respective contractual obligations with foreign franchises. We will have discussions with the players during the course of the week.”